The real crystal structure of a compound is defined by a deviation of the average structure caused by different types of defects. Extended defects, such as grain boundaries and dislocations influence the structure on a grand scale, without a variation on the level of individual unit cells. Small defects like single, isolated point defects, or correlated defects forming small defect-clusters, generally cause systematic variations of unit cells, which can be detected by diffraction methods. The method of average neutron-scattering length is an approach that gives a pos­sible solution of point defects. By this method it is possible to determine the cation distribution within the material for a wide range of structure types, and will be explained here using CuInSe2 and CuGaSe2 as examples.

The approach is based on the fact, that vacancies (VCu and VIn), as well as anti­site defects (InCu and CuIn), will change the neutron-scattering length of the cation sites 4a (copper site) and 4b (indium site) in the chalcopyrite-type structure sig­nificantly [15]. In a neutron diffraction experiment, the neutron interacts with the atomic nucleus and the neutron-scattering lengths of copper and indium are dif­ferent (bCu = 7.718 (4) fm, bIn = 4.065 (2) fm, bV = 0 [18]). Thus, the distribution of copper and indium on both cation sites of the structure can be revealed from the SOFs determined by Rietveld analysis of the neutron diffraction data.

If different species like Cu, In, and vacancies occupy the same structural site j, the average neutron-scattering length of this site is defined by:

bj = NCuj ■ bCu + Ninj ■ bIn + Nvj ■ bv (5.1)

Here, N is the fraction of the species on the corresponding site and b are the neutron-scattering lengths. As an additional requirement the full occupation of the site j has to be taken into account, which is achieved when ^2 Ni = 1 (i = Cu, In, V). In an example case the chalcopyrite-type crystal structure is used as basis model for the Rietveld refinement. Thereby, Cu occupies the 4a and In the 4b site. An experimental average neutron-scattering length for the two sites using the SOFs can be calculated by:

be4xap = SOF4a ■ bCu be4xap = SOF4b ■ bn (5.2)

where SOF4a and SOF4b are the cation site occupancy factors of the chalcopyrite — type crystal structure from the Rietveld analysis. The evaluation of the experimental average neutron-scattering length of a series of different Cu/In ratios, and therefore different degrees of off-stoichiometry, reveals a decrease of bff (see Fig. 5.6) with

decreasing Cu/In. Taking into account bV < bIn < bCu, a decrease of b4XT can only be caused by the presence of vacancies (VCu) or anti-site defects of type InCu. Since the decrease of b4XT becomes stronger with decreasing Cu/In, an increase of the par­ticular defect concentration can be assumed. Clearly, the value for b4b increases with decreasing Cu/In ratio. This can only be due to the presence of anti-site defects of type InCu (bCu > bIn).

The experimental average neutron-scattering lengths have to be compared with theoretical values. In a first step, these values are derived from a cation distribution model built on the basis of the known chemical composition of the material. The general formula for the calculation of the cation distribution is given by Eq. (5.1). A simultaneous comparison of bj with bjxp during variation of the cation-distribution model leads to the corresponding amounts of isolated point-defects.

Using this approach it was possible to determine the cationic point-defect con­centration for various chalcopyrite-type compounds. It was clearly shown that CuInSe2 tends, when being Cu-poor, to form VCu, InCu, and CuIn defects, resulting in a partially disordered chalcopyrite-type crystal structure. In contrast to CuInSe2, CuGaSe2 exhibits the same crystal structure, but due to the small ionic radii of Ga3+ [23] the material tends to form interstitial defects of type Gaj [24]. These differences sensitively influence the properties of a final solar device. The kind of point defects present in CuInSe2 allow a neutralization of isolated point-defects by clustering together forming a neutral defect complex of type (2VCu + InCu), which has a considerable binding-energy [16]. Such a neutralization of point defects cannot be assumed for CuGaSe2. This crucial difference is one reason why it is possible to design a thin-film solar cell with a very off-stoichiometric absorber and high defect — concentration, like CuInSe2, but maintain considerable efficiency. Tailoring high efficiency devices with a CuGaSe2 absorber layer is still a challenging task due to different problems. One aspect is the difference in the presence of intrinsic point — defects in Cu-poor CuGaSe2 discovered by neutron powder diffraction.